Fixed point theorems in generalized Hilbert spaces

Some fundamental fixed point theorems are proved for locally convex spaces whose generating family of seminorms satisfies the parallelogram law.     

求解复杂湍流的非线性涡黏性系数模型和代数应力模型

非线性涡黏性系数模型和代数应力模型联系了线性涡黏性系数湍流模型和完整的微分 雷诺应力模型.随着它们受到日益关注,其形式也越来越多样化.本篇综述的目的是对这些模 型加以总结并比较它们之间的共同点及不同之处,指出它们与完整微分雷诺应力模型之间的 关系,以及相对于线性涡黏性系数模型而言它们在预报流场上所具有的优势.     

Composition of stable set polyhedra

Barahona and Mahjoub found a defining system of the stable set polytope for a graph with a cut-set of cardinality 2. We extend this result to cut-sets composed of a complete graph minus an edge and use the new theorem to derive a class of facets.     

Tumour evolution inferred by single-cell sequencing

Genomic analysis provides insights into the role of copy number variation in disease, but most methods are not designed to resolve mixed populations of cells. In tumours, where genetic heterogeneity is common, very important information may be lost that would be useful for reconstructing evolutionary history. Here we show that with flow-sorted nuclei, whole genome amplification and next generation sequencing we can accurately quantify genomic copy number within an individual nucleus. We apply single-nucleus sequencing to investigate tumour population structure and evolution in two human breast cancer cases. Analysis of 100 single cells from a polygenomic tumour revealed three distinct clonal subpopulations that probably represent sequential clonal expansions. Additional analysis of 100 single cells from a monogenomic primary tumour and its liver metastasis indicated that a single clonal expansion formed the primary tumour and seeded the metastasis. In both primary tumours, we also identified an unexpectedly abundant subpopulation of genetically diverse 'pseudodiploid' cells that do not travel to the metastatic site. In contrast to gradual models of tumour progression, our data indicate that tumours grow by punctuated clonal expansions with few persistent intermediates.